1. Expand `(2x-1)(4x+5)`

Solution:
`(2x-1)(4x+5)`

FOIL method : `(a+b)(c+d)=ac+ad+bc+bd`

`=(color{red}{2x}+color{blue}{(-1)})(color{green}{4x}+color{purple}{5})`

`=color{red}{2x}*(color{green}{4x}+color{purple}{5})+color{blue}{(-1)}*(color{green}{4x}+color{purple}{5})`

`=color{red}{2x}*color{green}{4x}+color{red}{2x}*color{purple}{5}+color{blue}{(-1)}*color{green}{4x}+color{blue}{(-1)}*color{purple}{5}`

`=8x^2+10x+(-4x)+(-5)`

`=8x^2+6x-5`

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2. Expand `(3x-1)(2x-3)`

Solution:
`(3x-1)(2x-3)`

FOIL method : `(a+b)(c+d)=ac+ad+bc+bd`

`=(color{red}{3x}+color{blue}{(-1)})(color{green}{2x}+color{purple}{(-3)})`

`=color{red}{3x}*(color{green}{2x}+color{purple}{(-3)})+color{blue}{(-1)}*(color{green}{2x}+color{purple}{(-3)})`

`=color{red}{3x}*color{green}{2x}+color{red}{3x}*color{purple}{(-3)}+color{blue}{(-1)}*color{green}{2x}+color{blue}{(-1)}*color{purple}{(-3)}`

`=6x^2+(-9x)+(-2x)+3`

`=6x^2-11x+3`

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3. Expand `(7x+5)(4x+3)`

Solution:
`(7x+5)(4x+3)`

FOIL method : `(a+b)(c+d)=ac+ad+bc+bd`

`=(color{red}{7x}+color{blue}{5})(color{green}{4x}+color{purple}{3})`

`=color{red}{7x}*(color{green}{4x}+color{purple}{3})+color{blue}{5}*(color{green}{4x}+color{purple}{3})`

`=color{red}{7x}*color{green}{4x}+color{red}{7x}*color{purple}{3}+color{blue}{5}*color{green}{4x}+color{blue}{5}*color{purple}{3}`

`=28x^2+21x+20x+15`

`=28x^2+41x+15`

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4. Expand `(2x-5)(x^2+3)`

Solution:
`(2x-5)(x^2+3)`

FOIL method : `(a+b)(c+d)=ac+ad+bc+bd`

`=(color{red}{2x}+color{blue}{(-5)})(color{green}{x^2}+color{purple}{3})`

`=color{red}{2x}*(color{green}{x^2}+color{purple}{3})+color{blue}{(-5)}*(color{green}{x^2}+color{purple}{3})`

`=color{red}{2x}*color{green}{x^2}+color{red}{2x}*color{purple}{3}+color{blue}{(-5)}*color{green}{x^2}+color{blue}{(-5)}*color{purple}{3}`

`=2x^3+6x+(-5x^2)+(-15)`

`=2x^3-5x^2+6x-15`

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5. Expand `(2x-1)(x+5)`

Solution:
`(2x-1)(x+5)`

FOIL method : `(a+b)(c+d)=ac+ad+bc+bd`

`=(color{red}{2x}+color{blue}{(-1)})(color{green}{x}+color{purple}{5})`

`=color{red}{2x}*(color{green}{x}+color{purple}{5})+color{blue}{(-1)}*(color{green}{x}+color{purple}{5})`

`=color{red}{2x}*color{green}{x}+color{red}{2x}*color{purple}{5}+color{blue}{(-1)}*color{green}{x}+color{blue}{(-1)}*color{purple}{5}`

`=2x^2+10x+(-x)+(-5)`

`=2x^2+9x-5`

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